Field of the Invention
The present invention is related to selecting a field development plan based on a stochastic response surface.
Background Description
A typical state of the art development plan selected for a hydrocarbon reservoir field provides production guidelines for a given planning horizon on a drilling schedule to maximize production, i.e., to recover reservoir contents. Thus, evaluating oil and gas production potential and economic performance over a wide range of alternate field development plans for a particular reservoir is crucial to making good decisions. When geological and petro-physical properties are known, expensive reservoir flow simulators can estimate production potential and economic performance to model any given reservoir for fairly precisely evaluating the reservoir over differing field development plan alternatives.
Normally however, available reservoir information is limited. Typically, the geological and petro-physical properties carry a quantifiable uncertainty. Consequently, major investment decisions normally are made on field development plan models that are based on this limited and uncertain information. To adequately characterize the risks associated with property uncertainties standard reservoir production models necessarily consider a large set of possible reservoir realizations across property ranges for the different properties. For example, different geological and petro-physical have property ranges that vary between best case, nominal and worst case, independently or semi-independently, of every other property. For a particular reservoir, a set of reservoir realizations and associated probabilities characterize the uncertainty associated with geological and petro-physical properties.
Consequently, arriving at a thorough evaluation of a large number of decision variables with an even larger set of reservoir realizations has been required for selecting a field development plan. Indeed evaluating all decision variable combinations and reservoir realizations using expensive reservoir simulations has been time-consuming and, frequently, an intractable activity. Moreover, ultimately selecting a single realization is somewhat arbitrary and does not appropriately reflect the geological and petro-physical uncertainty involved.
Typical risk metrics conservatively quantify economic performance using a worst case measure, e.g., Value at Risk (V@R). A typical economic performance metric is the Net Present Value (NPV), which is time varying and depends on oil and gas production profiles. Production profiles for determining NPV derive from decision variables in reservoir simulation. Since geological and petro-physical properties are different for each reservoir realization, the NPV evaluated at a given decision variable is uncertain and has a probability distribution defined by the reservoir realizations.
For example, a decision maker with a risk neutral attitude, an attitude of indifference to risk, may represent reservoir economic value for a specific field development plan as an average NPV over all reservoir realizations. By contrast another, risk averse decision maker, taking an extremely conservative approach, may represent the reservoir economic value for the same field development plan with the worst case NPV (maximum production for the minimum realizations) across all possible reservoir realizations. Thus, utility/risk measures representing the NPV valuation have depended on the risk attitude of the decision maker.
State of the art field development plan evaluation approaches have combined a set of statistical and mathematical tools, known in the art as Design of Experiments (DoE) and Response Surface Methodologies (RSM). In particular DoE identifies the most influential decision variables that affect reservoir response, and uses those decision variables to determine a representative set of candidate configurations. Initially, RSM began with choosing specific statistical/risk measures, e.g., expected value and standard deviation, to construct surrogates. Then, RSM iteratively constructs a surrogate reservoir from the DoE configuration set that approximates the reservoir as a system response within a region of interest. For example, before determining a surrogate for the standard deviation of NPV, RSM required the standard deviation for simulation results over all geological realizations for each candidate configuration of input decision variables. RSM fit those standard deviations to a mathematical model as a function of the decision variables. Thus, RSM used an aggregated approach to reflect both system performance and associated risk in surrogates. With each geological realization, however, the RSM model lost the specific response of that reservoir realization to the decision variables, which led to an inaccurate risk assessment for the reservoir.
DoE and RSM have been particularly useful where system response evaluation is computationally expensive, e.g., when evaluation requires complex reservoir flow simulations. Even so, because of the large number of expensive reservoir simulations to cover all potential combinations of reservoir realizations and decision variables may be intractable due to a possibly large number of reservoir realizations. Thus, evaluating the response for every different decision and analyzing each different reservoir realization, i.e., each input decision variable configuration, has required a large number of expensive, time consuming reservoir flow simulations. Frequently, this has proven to be intractable, especially where geological uncertainty has required a very large number of such evaluations.
An individual surrogate constructed for each selected geological realization captures the appropriate stochastic behavior of the response to decision-maker (oil company) risk preferences. Indeed, if the selected reservoir realizations are truly representative of the population and the surrogate accurately approximates the dynamic behavior of each selected realization, any descriptive statistics or even risk measures will be well approximate by surrogates constructed realization-wise. Even after selecting a surrogate, however, evaluating it is relatively inexpensive, consuming relatively little computing resources and costs to evaluate it. The surrogate may be searched relatively easily to identify a new candidate decision point for a potentially enhanced response. However, verifying surrogate accuracy has required re-simulating at each new point. Verified simulation results could be used for yet another iteration to further improve the surrogate. For these state of the art approaches, however, changing the objective function required re-starting, and constructing a new surrogate from the beginning, which has been time consuming and required significant and potentially prohibitively expensive resources. Still other state of the art approaches have evaluated every decision point (i.e., each distinct configuration of the decision variables) for every geological realization, using expensive reservoir simulations that carry high computational costs.
Thus, given volatility of results from the progressive nature of RSM surrogate construction combined with the subjective and changing nature of decision makers' attitudes to risk, there is a need for an approach to constructing reservoir surrogates that are independent of chosen risk measures.